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# M23-10

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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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16 Sep 2014, 01:18
00:00

Difficulty:

5% (low)

Question Stats:

81% (00:39) correct 19% (00:48) wrong based on 135 sessions

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There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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16 Sep 2014, 01:18
Official Solution:

There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

The number of red roses must be a multiple of 21. It cannot be 42 or larger because this would mean that the number of white roses is 8 or larger and the total number of roses is 50 or larger. Because there are only 48 roses in the garden, the number of red roses is 21 and the number of white roses is 4. The number of black roses $$= 48 - 21 - 4 = 23$$.

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Intern
Joined: 24 Oct 2016
Posts: 29

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30 Sep 2017, 23:42
This is a high quality question.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82

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01 Oct 2017, 00:42
Bunuel wrote:
There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

let the red and white roses be $$21x$$ & $$4x$$

Hence Black rose $$= 48-(21x+4x) = 48-25x$$

Now $$x=1$$, because at $$x=2$$, no of black roses will be negative which is not possible

Hence no of black rose $$= 48-25=23$$

Option $$D$$
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Joined: 13 Feb 2018
Posts: 56

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27 Feb 2018, 08:13
Is this so called 700+ Question?
Math Expert
Joined: 02 Sep 2009
Posts: 46291

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27 Feb 2018, 10:15
LevanKhukhunashvili wrote:
Is this so called 700+ Question?

You can check difficulty level of a question along with the stats on it in the first post. For this question Difficulty: 600-700 Level. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.
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Re: M23-10   [#permalink] 27 Feb 2018, 10:15
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# M23-10

Moderators: chetan2u, Bunuel

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